查询词典 existence theorem of implicit function

Rader's algorithm, exploiting the existence of a generator for the multiplicative group modulo prime N, expresses a DFT of prime size n as a cyclic convolution of size N 1, which can then be computed by a pair of ordinary FFTs via the convolution theorem (although Winograd uses other convolution methods).

Rader演算法提出了利用点数为N的DFT进行长度为N-1的回旋摺积来表示原本的DFT，如此就可利用摺积用一对基本的FFT来计算DFT。

An existence theorem concerning denumerable 1-homoclinic orbits and countable families of 1-periodic orbits was given under a generic condition; and an intuitionistic de script ion about those orbits was also given.

证明在通有条件下，该异宿环附近存在可数无穷多条1-同宿轨，和可数无穷多个1-周期轨的单参数族，同时对这些周期轨和同宿轨作了直观描述。

What differ from that of the researchers in the past is the consideration of the direction of Hopf bifurcation with Dirichlet boundary condition , that is, the conditions when the Hopf bifurcation periodic solutions are orbitally asymptotically stable with asymptotic phase.Our basic idea come from the results given by Tang[30]. We adopt the method used by Hassard in the Hopf bifurcation theorem in [24], which is to judge the existence and the direction of Hopf bifurcation, and the stability of the Hopf bifurcation periodic solutions.

与以前的研究者不同的是，本文不仅讨论了在Dirichlet边界条件下系统的Hopf分支在以扩散系数为分支参数的情况下的存在性和分支周期解的空间非齐次性，而且更多的关注了系统在Dirichlet边界条件下Hopf分支解的稳定性及Hopf分支的方向，也即系统定态解在何种条件下，当分支参数如何变化时产生Hopf分支且分支周期解是带渐近位相轨道渐近稳定的。

In Chapter 1, we use the upper and lower solutions method, the bootstrap technique and the Schauder fixed point theorem to investigate the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems of the following three types:(1) Quasimonotone nondecreasing system;(2) Mixed quasimonotone system;(3) A nonquasimonotone 2-system. The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

A new complete disjunctive normal form, which is in the sense of equivalence, to an extension system of medium logical proposition calculus MP is defined and the theorem of its existence and uniqueness is established and proved.

讨论中介逻辑命题演算扩张系统MP＊中在等值意义下的完全析取范式的存在性和唯一性。引入MP＊中等值全析范式的概念，并用分步构造法证明这种范式在等值意义下是存在的，且是唯一的。

In this paper, the authors consider the even-order neutral difference equations with continuous arguments. By using Lebesgue' dominated convergence theorem, a necessary and sufficient condition for the existence of eventually positive and bounded solutions is obtained.

研究一类具连续变量偶数阶中立型时滞差分方程，利用Lebesgue控制收敛定理给出这类方程存在最终有界正解的一个充分必要条件，得到相应新的比较定理。

In this paper, a semilinear elliptic equation with critical Sobolev-Hardy exponents is studied, the existence of nontrival solutions for which is proved by the linking theorem in variational calculus.

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程，运用变分理论中的环绕定理证明了方程非平凡解的存在性。

Oseledec\'s Multiplicative Ergodic Theorem does not only solve the existence of Lyapunov exponents, but also show much more information of the dynamical structure.

Oseledec的乘法遍历定理解决了Lyapunov指数的存在性问题，并对动力系统的动力学结构给出了更多的信息，它现在已成为动力系统理论的最基本定理之一。

Chapter 3 This chapter is devoted to making further discussion to the existence theorem of essential components.

第二章 研究一些经济模型的平衡点的本质连通区的存在性。

We discuss the model, presentsome properties of the model, and show the existence theorem of the solution.

分析了模型的基本性质，证明了解的存在性。

When this condition occurs, inbound replication with the source partner is stopped on the destination domain controller and event ID 2042 is logged in the Directory Services event log.

计算机密码学是研究计算机信息加密、解密及其变换的科学，是数学和计算机的交义学科，也是一门新兴的学科。

Instructions: click on the thumbnails to see a larger image, then use the left-right arrow keys to scroll through the slideshow.

使用说明：滑鼠点在小图上即可放大观赏。开启后键盘左右键可用来换照片。